Hi! I need help to solve a task.
Write an equation of hyperbola. Foci coincides with the ellipse (x^2/35+y^2/10=1) focal points. There is given also a point from hyperbola - L(5sqrt(2);4)
Thanks for help in advance.
1. With an ellipse the foci have the coordinates with
That means the foci are at and
2. A hyperbola is defined by a constant difference of the distances between a point L on the hyperbola and the foci:
with
I've got
3. The excentricity of a hyperbola is calculated by:
Since the excentricity is e = 5 you can determine the value of b.
I've got
(For this part I used my computer)
4. Therefore the equation of the hyperbola is:
5. I've attached a drawing of the ellipse and the hyperbola with the point L on the right branch.